Alladi Ramakrishnan Hall

Consequences of Integrable Representations on Chern-Simons Theory

Arghya Chattopadhyay

IISER, Bhopal

Partition function for Chern-Simons(CS) theory on any Seifert manifold M with a gauge group
G and level K can be written as a sum over integrable representations of the corresponding affine
Lie algebra of the boundary Wess-Zumino-Witten Model. We consider the partition function
for U(N) Chern-Simons theory with level K written as a sum over Integrable representation(for
odd K) at large N, and show a natural manifestation of matrix integrals for CS theory studied
earlier.
For small coupling the dominant representations are characterised by Young diagrams with
number of boxes on the top-most row being less than the level K. On the other hand at some
critical value of the coupling, the dominant representations are always characterised by Young
diagrams with exact K number of boxes on the topmost row. The restriction over representations
dictate some constraints on the eigenvalue distribution of the matrix model as well. For CS theory on S2 × S1
this approach naturally describes the discreteness of the eigenvalues of the corresponding holonomy matrix which in turn translates into emergence of new phases. Our ongoing work deals with the effect of discreteness of the eigenvalues for the CS theory on S3.